Mac Internal Speakers Not Working, Audio Output Stuck in Headphones Mode

My Macbook Pro is not outputting any sound to the internal speakers, including system sounds like the charging sound, when nothing is connected to the headphone jack. Sound can be heard through headphones connected to the headphone jack. Only headphones show up in the sound preferences menu, and internal speakers DO NOT show up at all. There is NO red light illuminated inside the head phone jack.

I am using a 15-inch 2016 Macbook Pro (2.6 GHz i7, 512 GB storage, and 16 GB RAM) running on macOS High Sierra 10.13.6 (latest version). I tried following this support article to fix the issue: https://support.apple.com/en-us/HT203186.

I have so far tried turning up the volume, restarting my Mac, testing sound functionality on another user account, resetting the PRAM/NVRAM, resetting the SMC, restarting the coreaudiod process in Activity Monitor, blowing into the headphone jack to get rid of dust, and inserting a toothpick into the headphone jack, but none of this has solved the issue. I included 2 relevant screenshots below, it looks like the internal speakers are not even showing up in the system information menu. I am not sure why my Macbook Pro states that headphones are always connected, unless there is a problem with a switch in the headphone jack.

I would greatly appreciate any advice or tips for fixing this problem!